Probability question (boys & girls)

Hi, I'm new to this site. Sorry I'm jumping in with a question as the first post!

There was a question in my textbook that goes like this:
"A family has 2 kids. Given that at least one of them is a boy, what is the probability that both of them are boys?"

My idea was this:
Initially the kids could satisfy one of three cases:
boy/boy, boy/girl, girl/girl
But now that we are given that at least one of them is a boy, we can eliminate the case girl/girl. Out of the two remaining cases, one is favorable, so the probability should be 1/2.